Speakery research focuses on mathematical analysis, algorithm development, and their applications in machine learning and scientific computing, spanning both data and physical sciences. My Ph.D. training was grounded in classical numerical methods for partial differential equations (PDEs), with a particular emphasis on finite element methods (FEM) and multigrid methods. Armed with this solid fo...
Abstract:We will review physics-informed neural network and summarize available extensions for applications in computational mechanics and beyond. We will also introduce new NNs that learn functionals and nonlinear operators from functions and corresponding responses for system identification. The universal approximation theorem of operators is suggestive of the potential of NNs in learning fro...
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